The premise is that two energy fields influence all motion in classical physics. The first is the omnipresent Cosmic Background, the existence of which has been suspected for over a century, but with significant disagreement on the intensity. The second is the Mass Energy Field (ME) hypothesis on the existence of a localised energy field around every particle with mass and/or momentum. The spatial integral of the ME field for every massed particle is given by Einstein’s Mass Energy Equivalence Principle. The ME model leads to startling simplifications of several problems of significance of the past century that were considered almost intractable and required genius innovations: Einstein’s General Relativity (in the Solar System), 1916; Dirac Wave Function, 1928; and the Lamb Shift, 1947. The ME solutions, based on classical physics and conforming to Special Relativity, are simple, compact and do not require spacetime curvature, vacuum fluctuations, or renormalisation. For micro particles the ME model indicates a possible analytic expression for the Casimir Force, Lamb Shift, and the Strong Nuclear Force. The ME field around a massed particle, and the similar momentum energy field around a photon provide a plausible explanation for the century old vexing conundrum of wave-particle duality and points to a possible communication mechanism between quantum entangled particles. The Muon g-factor, computed with the ME expression, very different from existing QED theory, agrees with the measured value to 12 parts per billion. The ME theory shows exact agreement with General Relativity effects within the Solar System.